Which choices are solutions to the following equation? Check all that apply. X^2-10x-5=9

1. The figure shows the regular triangular pyramid SABC. The base of the pyramid has an edge AB = 6 cm and the side wall has an

Musya8 [376]

Given:

• AB = 6 cm

,

• SM = √15 cm

Let's solve for the following:

• 1) the base elevation AM.

Given that we have a regular triangular pyramid, the length of the three bases are equal.

AB = BC = AC

BM = BC/2 = 6/2 = 3 cm

To solve for AM, which is the height of the base, apply Pythagorean Theorem:

$\begin{gathered} AM=\sqrt{AB^2-BM^2} \\ \\ AM=\sqrt{6^2-3^2} \\ \\ AM=\sqrt{36-9} \\ \\ AM=\sqrt{27} \\ \\ AM=5.2\text{ cm} \end{gathered}$

The base elevation of the pyramid is 5.2 cm.

• (2)., The elevation SO.

To find the elevation of the pyramid, apply Pythagorean Theorem:

$SO=\sqrt{SM^2-MO^2}$

Where:

SM = √15 cm

MO = AM/2 = 5.2/2 = 2.6 cm

Thus, we have:

$\begin{gathered} SO=\sqrt{(\sqrt{15})^2-2.6^2} \\ \\ SO=\sqrt{15-6.76} \\ \\ SO=2.9\text{ cm} \end{gathered}$

Length of SO = 2.9 cm

• (3). Area of the base:

To find the area of the triangular base, apply the formula:

$A=\frac{1}{2}*BC*AM$

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*6^*5.2 \\ \\ A=15.6\text{ cm}^2 \end{gathered}$

The area of the base is 15.6 square cm.

• (4). Area of the side surface.

Apply the formula:

$SA=\frac{1}{2}*p*h$

Where:

p is the perimeter

h is the slant height, SM = √15 cm

Thus, we have:

$\begin{gathered} A=\frac{1}{2}*(6*3)*\sqrt{15} \\ \\ A=34.86\text{ cm}^2 \end{gathered}$

• (5). Total surface area:

To find the total surface area, apply the formula:

$TSA=base\text{ area + area of side surface}$

Where:

Area of base = 15.6 cm²

Area of side surface = 34.86 cm²

TSA = 15.6 + 34.86 = 50.46 cm²

The total surface area is 50.46 cm²

• (6). Volume:

To find the volume, apply the formula:

$V=\frac{1}{3}*area\text{ of base *height}$

Where:

Area of base = 15.6 cm²

Height, SO = 2.9 cm

Thus, we have:

$\begin{gathered} V=\frac{1}{3}*15.6*2.9 \\ \\ V=15.08\text{ cm}^3 \end{gathered}$

The volume is 15.08 cm³.

ANSWER:

• 1.) 5.2 cm

,

• 2.) 2.9 cm

,

• 3.) 15.6 cm²

,

• 4.) 34.86 cm²

,

• (5). 50.46 cm²

,

• 6). 15.08 cm³.

7 0

1 year ago

g Using calculus and the SDT (then FDT if necessary), find all global and local maximum and minimums given the function f(x) = x

iren [92.7K]

Answer:

$S_{1 } (x,y) = (0.333, 0.815)$ (Absolute minimum) and $S_{2} (x,y) = (-1, 2)$ (Absolute maximum)

Step-by-step explanation:

The critical points are determined with the help of the First Derivative Test:

$f'(x) = 3\cdot x ^{2} +2\cdot x -1$

$3\cdot x^{2} + 2\cdot x - 1 = 0$

The critical points are:

$x_{1} \approx 0.333$ and $x_{2} \approx -1$

The Second Derivative Test offers a criterion to decide whether critical point is an absolute maximum and whether is an absolute minimum:

$f''(x) = 6\cdot x +2$

$f''(x_{1}) = 3.998$ (Absolute minimum)

$f''(x_{2}) = -4$ (Absolute maximum)

The critical points are:

$S_{1 } (x,y) = (0.333, 0.815)$ (Absolute minimum) and $S_{2} (x,y) = (-1, 2)$ (Absolute maximum)

7 0

3 years ago

What is 4/9 divided by 2/3 divided by 5/6

joja [24]

(4/9) divided by (2/3) is 2/3 because you do the reciprocal and mul. Then you mult it by the reciprocal of (5/6) which is (6/5) and get 4/5

7 0

4 years ago

Read 2 more answers

The sum of the measures of angles K and L is 1

Pavlova-9 [17]

Answer:

43 is your answer.....

8 0

4 years ago

1 Find the shaded area for each of the following shapes.

andrew-mc [135]

Answer:

the answer is 40

7 0

4 years ago